Answer:
There are 12 sets of four marbles include all the red ones.
Step-by-step explanation:
Given : A bag contains three red marbles, two green ones, one lavender one, four yellows, and five orange marbles.
To find : How many sets of four marbles include all the red ones?
Solution :
Number of red marbles = 3
Number of green marbles = 2
Number of lavender marbles = 1
Number of yellow marbles = 4
Number of orange marbles = 5
We have to form sets of four marbles include all the red ones,
For position of getting red ones we have three red marbles i.e. ![^3C_3](https://tex.z-dn.net/?f=%5E3C_3)
For the fourth one we have 12 choices i.e. ![^{12}C_1](https://tex.z-dn.net/?f=%5E%7B12%7DC_1)
Total sets of four marbles include all the red ones is
![=^3C_3\times ^{12}C_1](https://tex.z-dn.net/?f=%3D%5E3C_3%5Ctimes%20%5E%7B12%7DC_1)
![=1\times 12](https://tex.z-dn.net/?f=%3D1%5Ctimes%2012)
![=12](https://tex.z-dn.net/?f=%3D12)
Therefore, There are 12 sets of four marbles include all the red ones.